A094545 Number of minimal T_0-covers of an n-set.

1, 1, 1, 4, 17, 176, 2287, 49540, 1518337, 67457584, 4254836111, 376795261844, 46709151254449, 8061849904932136, 1936383997541071639, 646603398091877815516, 300476951799493029958913

Offset: 0

Author

Goran Kilibarda and Vladeta Jovovic, May 08 2004

Keywords

• easy
• nonn

Comments

A cover of a set is a T_0-cover if for every two distinct points of the set there exists a member (block) of the cover containing one but not the other point.

Row sums of A094544.

Links

• Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
• Eric Weisstein's World of Mathematics, Minimal Cover.

Crossrefs

Cf. A035348, A046165, A094544, A094546.

Formula

a(n) = Sum_{m=0..n} (n!/m!)*binomial(2^m-m-1, n-m).

a(n) = Sum_{m=0..n} Stirling1(n, m)*A046165(m).

E.g.f.: Sum_{n>=0} x^n*(1+x)^(2^n-n-1)/n!.